Method and apparatus for providing professional liability coverage

ABSTRACT

A system and method are provided that, in the case of professionals having large numbers of publicly traded corporate clients, are able to use the relative probabilities of different ones of those clients suffering a professional liability triggering event and the likely relative impact of such an event on different clients, to provide professional liability coverage at either lower cost to the professional or higher profits to the provider. The right to deliver securities in the publicly traded client companies at any time during the coverage period, at the price in effect at the starting date, is secured. The covered professional or its insurer is granted the qualified right to sell those securities at the starting price. If the value of a company falls because of a professional liability triggering event, the covered party is allowed to exercise that right to sell. To exercise the right to sell, the party will be able to buy the securities at the then current reduced price, thus reaping as a gain substantially the amount of potential claims against it.

BACKGROUND OF THE INVENTION

This invention relates to a method and apparatus for providingprofessional liability coverage. More particularly, this inventionrelates to a method and apparatus for providing professional liabilitycoverage to professionals whose clients include a substantial number ofpublicly traded corporations with respect to whom a professionalliability triggering event causes a decline in stock price. Mostparticularly, this invention relates to such method and apparatus forusing the decline in stock price to offset the amount paid in claims bythe coverage provider to the covered professional.

Traditional insurance of any kind relies on statistics andprobabilities. The insurer insures a large number of insureds against aparticular peril, charging premiums to each and relying on thelikelihood that the peril will only come to pass for a small number ofthe insureds. As long as the premiums are high enough, the insurer willmake a profit after payment of any claims. Typically, the premiums willbe invested to generate additional income. An insurer may investigatepotential insureds to determine whether or not their behavior makes themmore likely than average to suffer the peril to be insured against,turning down those who exhibit risky behavior, or charging a higherpremium. In any event, however, ignoring investment income on premiumscollected, the insurer's profit depends on collecting more in premiumsthan it pays in claims. There is no other known mechanism for offsettingthose claims.

Professional liability insurance for professionals whose clients arelarge corporations and whose professional misconduct may result inmultimillion-dollar changes in the value of those corporations, is nodifferent from other insurance. Insurers write professional liabilitycoverage for such professionals and charge very large premiums, so thaton average they take in more in premiums than they pay in claims whenthere is a claim against the professional by the stockholders of such acorporation. For example, in the case of an accounting firm having majorcorporations as its clients, stockholders of one of those corporationsmay have a large claim against the firm in case of an auditfailure--i.e., the failure of an audit to uncover an irregularity thatshould have been uncovered, if the stockholders relied on the audit inmaintaining or increasing their holdings and the value of those holdingsfalls when the irregularity is discovered. Similarly, such a claim mayarise against a law firm if an ill-considered opinion is rendered to alarge corporation and is relied on by stockholders in the same way, andthen the value of their holdings falls when the subject matter of theopinion comes to pass.

For professionals having such large corporate clients, it ought to bepossible to determine, for each pairing of one client with any otherclient, the relative probabilities of different members of that pair ofclients suffering a professional liability triggering event--e.g., anaudit failure in the case of an accounting firm--and the likely relativeimpact on the members of that pair of clients. However, to date, thoserelationships have not been used to enhance the ability of an insurer,or other professional liability coverage provider, to provide suchcoverage at either lower cost to the professional or higher profits tothe provider.

It would be desirable in the case of professionals having large numbersof publicly traded corporate clients to be able to use the relativeprobabilities of different ones of those clients suffering aprofessional liability triggering event and the likely relative impactof such an event on different clients, to provide professional liabilitycoverage at either lower cost to the professional or higher profits tothe provider.

SUMMARY OF THE INVENTION

It is an object of this invention in the case of professionals havinglarge numbers of publicly traded corporate clients to use the relativeprobabilities of different ones of those clients suffering aprofessional liability triggering event and the likely relative impactof such an event on different clients, to provide professional liabilitycoverage at either lower cost to the professional or higher profits tothe provider.

In accordance with the present invention, there is provided a method ofproviding professional liability coverage to a professional, during acoverage period having a starting date and an ending date, when theprofessional has clients including a substantial number of publiclytraded corporations each having a respective securities price at arespective starting price on the starting date, and with respect to whoma professional liability triggering event could cause a decline in therespective securities price. The method includes determining arespective number of positions in securities of each of the publiclytraded corporations needed to provide the professional liabilitycoverage, based on market correlation between prices of securities ofthe publicly traded corporations, and on at least one of (a) theprobability that a professional liability triggering event will occurrelative to any one or more of said publicly traded corporations, and(b) likely effect of that professional liability triggering event on theprice of securities of the one or more publicly traded corporations. Ata respective cost a right is secured to deliver at a respective deliveryprice, at any time at least as late as the ending date, the respectivenumber of positions in securities of each of the publicly tradedcorporations. From the respective costs, a payment to be charged to saidprofessional in exchange for the coverage is determined. In exchange forthe payment, a right to sell, at a respective claim price, at any timeduring the coverage period, up to the respective number of positions insecurities of any one of the publicly traded corporations, when there isa professional liability triggering event with respect to any of saidpublicly traded corporations, is conferred on the covered party. Acoverage document setting forth the payment and evidencing the right tosell is generated.

Apparatus for performing the method is also provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the invention will beapparent upon consideration of the following detailed description, takenin conjunction with the accompanying drawings, in which like referencecharacters refer to like parts throughout, and in which:

FIG. 1 is a schematic view of a first preferred embodiment of a hardwaresystem according to the present invention;

FIGS. 2A and 2B (hereinafter collectively "FIG. 2") are a flowchartillustrating a preferred embodiment of the method according to thisinvention;

FIG. 3 is a flowchart illustrating a preferred embodiment of the minimumvariance portfolio determination step of the method illustrated in FIG.2;

FIG. 4 is a flowchart illustrating a preferred embodiment of the marketvalue index determination step of the method illustrated in FIG. 3; and

FIG. 5 is an illustration of a second preferred embodiment of a hardwaresystem according to the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is based on the existence, in the capital markets,of instruments and mechanisms that allow an investor not only topurchase shares of a publicly owned corporation or other securitiesrelated to the current value of a corporation (e.g., bonds, etc.), butalso to purchase the right to buy or sell securities at a later date ata fixed price and to sell securities that one does not own for deliveryat a later date. Examples of some of these latter types of instrumentsand mechanisms are puts (right to sell at a fixed price), calls (rightto buy at a fixed price), and short sales (sale for delivery at a laterdate). The invention is further based on the willingness of potentialinvestors to assume varying degrees of risk in trading in suchinstruments and relying on such mechanisms.

The invention provides professional liability coverage to professionalswho have as clients publicly traded corporations. Instead of relying onstatistical probabilities over a large number of clients and insureds asin the case of professional liability insurance, coverage providedaccording to the present invention takes advantage of the fact thatdamages, and therefore claims to be covered, in a professional liabilitysituation are based on a change in value of securities of the affectedclient, and uses that change in value itself to at least partially, ifnot totally, offset the claim to be paid. The coverage can be provideddirectly to the professional, but because the invention involves tradingin the very securities whose value has been adversely affected by analleged professional liability triggering event, and thus may give riseto ethical difficulties if the professional is seen as trading in thosesecurities, the coverage is more likely to be provided to an insurancecompany, in a manner analogous to reinsurance. The insurance companywould then provide a traditional professional liability insurance policyto the professional. However, the insurance company could make a largerprofit and still charge a lower premium to the professional, because itscosts would be lower as explained below, or it could further increaseits profits at the same level of premium.

In accordance with the invention, at the start of the coverage period,the coverage provider establishes positions in a basket of securities ofeach of the publicly traded clients of the professional to be covered.Typically, the securities will be shares of stock, but other securitiescould be used. The distribution of numbers of positions in thosesecurities (e.g., the relative number of shares of stock in each client)is selected in accordance with the invention by computing a minimumvariance portfolio of those securities, computed from an adjustedvariance-covariance matrix of those securities. The absolute number ofpositions (e.g., shares) depends on the amount of coverage required ordesired by the covered professional or the insurer.

The adjusted variance-covariance matrix is based on a standardvariance-covariance matrix, well known in portfolio theory. In such amatrix, the ijth term and the jith term reflect the expected performanceof the ith security relative to the jth security based on ordinarymarket relationships. For example, if all of the securities are issuedby companies in one industry, they would all be expected to rise or falltogether, and by about the same amount, and thus the ijth term and thejith term in the matrix would be about +1.0.

For companies in related, noncompeting industries, they would all beexpected to rise or fall together, but by differing amounts. Thus, e.g.,for automobile manufacturers and suppliers, the value of securities of asupplier might be expected to move in the same direction as that ofsecurities of a manufacturer, but, unless the supplier had nonon-automotive customers, the magnitude of the movement in value wouldbe different. In such a case, the ijth term and the jith term in thematrix would both be positive, but would have magnitudes other than 1.0.For example, the covariance of a steel company and an automobile companymight be about 0.2, because the steel company has other customers, andthus would not suffer a downturn in the automobile market to the sameextent as the automobile manufacturer.

For companies in competing industries, the terms would be negative, andthe magnitudes would vary. For example, if all travelers travel eitherby bus or by airplane, the covariance of a bus company and an airlinewould be -1.0. But because some travelers opt to drive themselves totheir destinations, the absolute value of the actual covariance is lessthan 1.0.

As set forth above, in accordance with the present invention, thestandard variance-covariance matrix is preferably adjusted. Theadjustments preferably are based on two factors. One factor on whichadjustments are preferably based is the relative probability of aprofessional liability triggering event occurring, and can be referredto as the triggering event index. For example, where the professional tobe covered is an accounting firm, the liability triggering event mightbe an audit failure. For the two companies represented by the ijth andjith terms, it is possible to assign a factor for the relativeprobability of an audit failure occurring. For example, if the ithcompany is a very large, very widely held company whose management ownsa small percentage of the company, and the jth company is a relativelysmall, closely held company whose management owns a large percentage ofthe company, the jth company would be more likely, statistically, thanthe ith company to suffer an audit failure, because of the greaterlikelihood of improperly documented transactions. That greaterlikelihood can be accounted for according to the present invention inseveral ways. One relatively simple way is to determine a factor bystatistical or actuarial methods that reflects the increased likelihoodof an audit failure for the jth company relative to the ith company andthen simply multiply both the ijth and jith terms by that factor as thetriggering event index. Alternatively, both terms could be divided bythat factor, or could be adjusted by a triggering event index derivedfrom those probabilities in a more complex way.

A particularly preferred mathematical representation of an audit failureindex AFI (for use where the professional is an accounting firm and thetriggering event is an audit failure) for a particular security is:

    AFI=a.sub.1 x.sub.1 +a.sub.2 x.sub.2 +a.sub.3 x.sub.3 +a.sub.4 x.sub.4 +a.sub.5 x.sub.5

where ##EQU1## and where each x_(i) is a factor related to the securityas follows: x₁ : The nature, stability, degree of competition, andgeneral economic health of the industry(ies) in which the entityoperates;

x₂ : Management's reputation, integrity, operating philosophy, financialstate, and prior operating results;

x₃ : The nature, age, size and operating structure of the entity;

x₄ : The control environment and significant management and accountingpolicies, practices and methods;

x₅ : The accounting system and control procedures; each x_(i) rangingfrom 1 to 10, with 1 being the best and 10 being the worst. Thesescoring scales are associated with the different degrees of difficultyin gathering and evaluating the evidentiary material, which is reflectedby the related weights a_(i). Accordingly, AFI can range from 1 to 10.

The second factor on which adjustments are preferably based is therelative amount by which the market value of the two companies would beaffected by a liability triggering event, and can be referred to as themarket value index. At least in the case where the professional is anaccounting firm, in computing the market value index, only the portionof the securities held by the general public, and not by management, isincluded. That is because any audit failure is likely the result ofimproper actions by management, and management would not have a cause ofaction against the accounting firm only the public stockholders wouldhave such a cause of action. However, it is possible that for certainprofessionals, the management stockholders of the corporation would alsohave a cause of action, and in such a case, the value of securities heldby management would be taken into account.

There are several ways to compute the market value index. For example,if the total value of publicly held securities of the ijth company isten times that of publicly held securities of the jith company, one orboth of the ijth and jith terms could simply be multiplied, or divided,by 10. However, the market value index in accordance with the presentinvention preferably is computed by taking a value about midway betweenthe two values, such as the average, or the median, of the two values,and then assigning as the market value index for the ijth term the ratioof the value of the ith company to that midway value, and assigning asthe market value index for the jith term the ratio of the value of thejth company to the midway value. Each term is then preferably multipliedby its assigned market value index.

Once the adjusted variance-covariance matrix has been formed, a minimumvariance portfolio can be determined using optimization techniques in amanner well known in portfolio theory. The optimization techniques thatare used generally have, underlying them, some form of differentiationto select a minimum variance. However, the technique applied directlymay resort to Lagrangian multipliers or other mathematical optimizationtechniques, or, increasingly commonly, numerical techniques which areespecially well-suited for digital computers.

The result of the optimization of the variance-covariance matrix will bea collection of coefficients or weights x_(ip) representing the relativequantities of securities in each company in which positions should beestablished to provide the desired coverage in accordance with theinvention. If the coefficients are normalized so that they total 1.0,that normalized set of coefficients could be thought of as representingone "unit" of professional liability coverage. The number of "units,"and thus the total number of securities of each company, in whichpositions are to be established would depend on the amount of coveragerequired of desired by the professional, as discussed below.

In a preferred embodiment of the invention, the computation of weightsassociated with the securities that comprise the client portfolio is avariant of a known portfolio selection model, whose form is:

Minimize σ² (R_(p)),

x_(ip), i=1, . . . , n

subject to constraints ##EQU2##

Where E(R_(e)) is some given level of expected return for the portfolio,σ² (R_(p)) stands for the variance of return of the portfolio taken as awhole, and E(R_(i)) stands for the expected return of security i. Theproblem stated in the equations is to choose proportions x_(ip), i=1, .. . , n, invested in individual securities that minimize the variance ofportfolio return subject to the constraints that expected portfolioreturn is equal to E(R_(e)) and that the sum of proportions invested inindividual securities is 1.0.

Similarly, the preferred form of the model according to the presentinvention is:

Minimize σ₂ (R_(p)),

x_(ip), i=1, . . . , n

subject to the constraints ##EQU3##

In this model σ² (R_(p))stands for the variance of exposure tomalpractice liability, E(R_(i)) denotes liability exposure associatedwith security i, and E(R_(e)) the liability exposure of the portfoliotaken as a whole.

The general approach to problems of the type described above is to firstform the Lagrangian expression ##EQU4## where 2λ_(e) and 2Φ_(e) are theLagrange multipliers for the constraints. Minimizing the variance ofportfolio return subject to the constraints involves differentiating theLagrangian expression with respect to 2λ_(e), 2Φ_(e) and x_(ip), i=1, .. . , n and setting these partial derivatives equal to 0.0. For 2λ_(e)and 2Φ_(e), this procedure simply tells us that the proportions investedin individual securities must satisfy the constraints. For the x_(ip),i=1, . . . , n, however, the procedure yields the n new conditions##EQU5## where x_(je), j=1, . . . , n, are the specific proportionsinvested in individual securities that define the minimum varianceportfolio with expected return E(R_(e)).

It can be shown that after appropriate manipulation and substitutionthat the following is a form of the equation that can be used:

    E(R.sub.j)=E(R.sub.oe)- E(R.sub.oe)-E(R.sub.e)!β.sub.ei, i=1, . . . , n,

where ##EQU6## in the risk of security i in the portfolio e measuredrelative to the risk of the portfolio. E(R_(oe)) represents theliability exposure that is uncorrelated with the portfolio of clients;it is in essence the maximum liability that the professionalorganization believes it is exposed to based on prior experience.

To account for the market value index referred to above, it ispreferable to redefine β_(ie) : ##EQU7## where P_(i) =price of securityi, and

P_(e) =an index which is the sum of the prices of the individualsecurities comprising the client portfolio.

It is also set forth to define Ex_(i) =P_(i) ·(total number of shares ofsecurity i held by non-insiders), which is an estimate of the maximumliability that a professional firm faces for the ith client. The totalexpected liability over all clients is: ##EQU8##

From the above elements, the coefficients x_(ip) are computed in thefollowing manner: ##EQU9##

At the start of the coverage period the coverage provider wouldpreferably secure the right to deliver in the future the number ofsecurities--e.g., shares of stock--required to provide the desiredcoverage. The right secured preferably would include the right todeliver those securities at any time during the coverage period. Theprice at which the securities are to be delivered preferably would bethe price as of the starting date of the coverage period (or some otherpredetermined delivery price). For example, the provider preferablycould sell the shares in the portfolio short at the starting price orsome other predetermined delivery price. The provider preferably wouldthen confer on the covered party--the professional or its insurer--theright to sell the shares in the portfolio at the starting price or someother agreed upon claim price. This right preferably also could beexercised at any time during the coverage period.

If a professional liability triggering event were to occur, and thevalue of the stock of the affected company dropped, the covered partycould go out into the market and purchase the affected shares at theirnew, low, post-event price. The covered party could then exercise itsright to sell those shares to the provider at the starting price orother agreed claim price. The covered party thus recovers the amount itis likely to owe in damages (the spread between starting price andpost-event price), and thus is now whole. The provider, who now owns theshares at their post-event price, is also whole because it can exercisethe right previously secured to deliver the shares at the originalstarting price or other predetermined delivery price.

The provider's profit, if any, is the result of the differential betweenthe starting price and the delivery price or other claim price. Theprovider may also charge a fee instead of, or in addition to, thatdifferential.

The right secured by the provider to deliver the shares at the startingprice usually also carries with it the obligation to do so. That wouldcertainly be the case if the mechanism used were the short saledescribed above. The provider may find itself in a difficult situationat the end of the coverage period if there has been no liabilitytriggering event and, through the normal course of events, the price ofthe portfolio has increased. Because there was no triggering event, theprovider will not have acquired the shares from the covered party andwill have to acquire them on the open market at the new higher price. Toavoid that situation, the provider, as part of securing the right todeliver the securities could also secure the right to acquire thesecurities at the starting price or some other predetermined buyingprice. For example, the provider could purchase a simple call option tobuy the required securities on the ending date of the coverage period atthe starting price or other buying price. The cost of the option, aswell as any differential between the starting price and the buyingprice, could be passed on to the covered party as part of the fee or"premium" for coverage.

The number of "units" required for coverage according to the inventionis determined by the amount of coverage desired by the covered party,expressed as both dollar amount and a percentage fall in value to becovered. For example, the covered party may want coverage of$10,000,000.00 for a 50% fall in value.

Given that the number of securities and price observations for a givensecurity will be significant, it is reasonable to assume that theportfolio of securities is a sample from a multivariate normalpopulation which is represented by: ##EQU10##

of constant density for the p-dimensional normal distribution areellipsoids defined by x such that ##EQU11##

These ellipsoids are centered at μ and have axes ±c√(λ_(i) e_(i)), whereΣe_(i) =λ_(i) e_(i), i=1, 2, . . . , p.

Beyond i=2, these hyperellipsoids become difficult to deal with. Thesolution is to collapse the multi-dimensional normal distribution to aunivariate normal distribution.

In the situation according to the invention the P_(i) (i.e., the pricesof security i) stand for the x_(i). Defining a univariate variable as##EQU12## then it could be standardized as ##EQU13##

There are tables for the standard normal variable Z.

For example, assume that in a given instance there are three securitieswith x=$17.42; σ² =141.76; σ=11.91 and that it is desired to ascertainan S that would satisfy the condition that is between x minus onestandard deviation (or lying at approximately the 16% level) and x plusone standard deviation (or lying at approximately the 84% level). Fromthe standard normal distribution tables:

    5.51=17.42-11.91

and

    29.33=17.42+11.91

Thus S can range from about 5.51 to about 29.33 and it would cover about84-16=68% of the probability space.

It remains to allocate the 11.91 increase or decrease in total price tothe hypothetical securities in the example. For this, the covariance ofeach security with the portfolio as a whole is calculated. Assume thatfrom the covariance for security i, i=1,2,3, the β_(ip) for eachsecurity is:

Security 1: β=5.37

Security 2: β=3.75

Security 3: β=2.88

Normalized, the betas become

Security 1: β=0.45

Security 2: β=0.31

Security 3: β=0.24

With these in hand one can compute the individual values of thesecurities that would sum to either the lower bound of 5.51 or the upperbound of 29.33:

    ______________________________________                                        Security 1:                                                                            6.25       -     5.36    =   0.89                                    Security 2:                                                                            6.25       -     3.69    =   2.56                                    Security 3:                                                                            4.92       -     2.86    =   2.06                                             17.42            11.91       5.51                                    Security 1:                                                                            6.25       +     5.36    =   11.51                                   Security 2:                                                                            6.25       +     3.69    =   9.94                                    Security 3:                                                                            4.92       +     2.86    =   7.78                                             17.42            11.91       29.33                                   ______________________________________                                    

The new values lie on the contour of the correct hyperellipsoid.

The covered party preferably would be issued a contract, certificate orother written evidence of having paid the "premium" and having receivedthe right to sell the securities at the agreed upon claim price (such asthe starting price).

If a covered party suffers a professional liability triggering event asto a particular client, the covered party would make a claim and,assuming that the event came within the terms of any applicable coverageagreement, the provider would allow the covered party to sell an amountof shares of the affected client up to the number represented by theunits purchased, at the starting price or other agreed upon claim price.The covered party would presumably have bought those shares on the openmarket at the post-event price. The provider would then exercise itsright to deliver those shares at the starting price or other agreed upondelivery price.

The covered party could find itself recovering more than it planned. Forexample, if the coverage selected was for a 50% fall in value, but theactual fall in value of the affected client was 75%, the covered partymight still be able to recover the full loss if there were othercompanies in the portfolio which declined in value in the normal courseof events. Unless the coverage agreement specifies that only securitiesof the affected client company can be sold at the starting price, thecovered party could sell at their respective starting prices shares ofunaffected clients that happened to have declined for other reasons,purchasing them first at their current lower price. It is preferred thatsuch sales be allowed. However, the right to sell preferably could onlybe exercised if a professional liability triggering event occurred withrespect to a client included in the portfolio, and not for other clientsoutside the portfolio, or when there has been no triggering event.

The coverage provided by the invention could be analogized to a new typeof security, which could be referred to as a specialized put option.Like a standard put option, it offers the right to sell at an agreedupon price, but it is specialized in that it is exercisable only on theoccurrence of a professional liability triggering event with respect toone of the companies in the portfolio.

The present invention also includes apparatus for implementing themethod just described. In addition to recordkeeping apparatus forkeeping track of covered parties, "premium" payments received, claimsmade and paid, etc., the apparatus according to the invention includesapparatus for computing the minimum variance portfolio, and specificallyfor calculating the triggering event index and the market value index.The minimum variance portfolio calculation apparatus can include aprogrammed general purpose computer, or it can be implement as aspecial-purpose logic circuit.

The present invention may be implemented on a variety of computersystems--ranging from a modest personal computer (such as one based onthe 80X86 series of microprocessors originally developed by IntelCorporation, of Santa Clara, Calif.) equipped with a spreadsheet programsuch as LOTUS® 1-2-3(available from Lotus Development Corporation, ofCambridge, Mass.) and other mathematical application programs such asMATHEMATICA® (available from Wolfram Research, Inc., of Champaign, Ill.)to a supercomputer, depending on the number of potential covered partiesand the specific mathematical techniques used to implement theinvention. An exemplary computer hardware system 10 with which thepresent invention may be implemented is shown in FIG. 1.

In FIG. 1, which shows a first preferred embodiment of apparatusaccording to the invention, system 10 includes a computer 11 comprisinga central processing unit ("CPU") 20, a working memory 22 which may be,e.g, RAM (random-access memory) or "core" memory, mass storage memory 24(such as one or more disk drives or CD-ROM drives), one or morecathode-ray tube ("CRT") display terminals 26, one or more keyboards 28,one or more input lines 30, and one or more output lines 40, all ofwhich are interconnected by a conventional bidirectional system bus 50.

Input hardware 36, coupled to computer 11 by input lines 30, may beimplemented in a variety of ways. Market value data, and other data suchas number of shares outstanding, may be inputted via the use of a modemor modems 32 connected by a telephone line or dedicated data line 34 toan online financial service. Alternatively or additionally, the inputhardware 30 may comprise CD-ROM drives or disk drives 24. In conjunctionwith display terminal 26, keyboard 28 may also be used as an inputdevice.

Output hardware 46, coupled to computer 11 by output lines 40, maysimilarly be implemented by conventional devices. By way of example,output hardware 46 may include CRT display terminal 26 for displayingthe payment to be charged or the mix of stocks of other securities thatmake up one unit of the minimum variance portfolio. Output hardwaremight also include a printer 42, so that hard copy output may beproduced, or a disk drive 24, to store system output for later use.Where asset trades are to be executed in order to provide coverage to asubscribing covered party, the trading information may be transmittedover telephone or dedicated data lines 34, possibly with the use ofmodem 32, to cause the trades to be executed.

In operation, CPU 20 coordinates the use of the various input and outputdevices 36, 46, coordinates data accesses from mass storage 24 andaccesses to and from working memory 22, and determines the sequence ofdata processing steps. Specific references to components of the hardwaresystem 10 are included as appropriate throughout the followingdescription of the processing steps carried out by the hardware system.

FIG. 2 shows one preferred embodiment 200 of the method according to theinvention, particularly as it might be implemented by apparatus 10 toprovide coverage to an accounting firm or its insurer. The system startsat step 201 where a potential covered party, such as an accounting firm(or its insurer)--although the invention applies to other professionals,as discussed above, makes an application for coverage. The applicationwould include, in addition to the usual information (name, address,etc.), a list of the publicly traded clients of the firm. Theapplication would also include the desired amount of coverage, expressedas both a dollar limit and a percentage of decline in value, asdiscussed above and in more detail below. In addition, the applicationwould specify the coverage period by starting date and ending date. Theusual coverage period would be one year. The application data wouldpreferably be entered by keyboard 28, although other entry devices, suchas optical character readers (not shown), may be used to scan theapplication, or the application may be provided in a machine readableformat for insertion into a disk drive 24 or for transmission over dataline 34 for reception via modem 32.

The system then proceeds to step 202, where a minimum variance portfolioof the publicly traded clients is determined, as discussed in moredetail below in connection with FIGS. 3 and 4. The minimum varianceportfolio represents the relative number of shares (or other securities)of each publicly traded client needed to provide coverage according tothe invention with minimum risk. When normalized so that thecoefficients sum to 1.0, the coefficients represent one "unit" ofcoverage. The dollar value of a unit depends on the values of theparticular stocks or other securities involved.

Next, the system proceeds to step 203 where the number of units isdetermined. As discussed above, the number of units is a function of thevalue of a unit and the dollar value of coverage required, as well asthe percentage loss to be covered. Specifically, the potential coveredparty, or applicant, will be asked to select both a dollar value ofcoverage desired, and the percentage drop in the value of a client'sstock price to be covered. For example, a client may want $30 million incoverage against the possibility that as the result of an audit failurea client's stock price will drop 40%. As discussed above, and in moredetail below, this is a partly statistical determination and the coveredparty may end up being covered for a greater loss. Alternatively, theapplicant may specify a desired cost of coverage and the number of unitswould then be determined simply by the price of a unit, as determinedbelow.

At step 204, the system secures the right to deliver the securitiesmaking up the desired number of units of the minimum variance portfolio.A preferred way, but not the only way, of accomplishing this result isto sell short the respective required number of shares of eachrespective company for delivery at any time prior to or on the endingdate of the coverage period at an agreed upon delivery price which ispreferably the starting price on the starting date. In addition, it ispreferable to purchase a call option securing the right to buy therequired number of shares at any time up to and including the endingdate at a buying price which preferably is the starting price. The calloption protects the coverage provider against the possibility that manyor all of the client companies will have risen in value during thecoverage period, so that when the time comes to deliver the shares soldshort, the provider will not have to purchase the required shares orother securities at the higher market price to deliver them at thestarting price.

At step 205, the system determines the payment (analogous to aninsurance premium) to be charged to the covered party. In this preferredembodiment, the payment would be the cost of the call option in step204, plus any transaction costs associated with the short sale (or othertransaction) in step 204, plus some profit margin for the coverageprovider. This payment can be much smaller than a traditional insurancepremium because the coverage provider does not need to worry aboutspreading risk over a number of covered parties with some probability ofclaims, and the need to be able to pay those claims and still make aprofit. Here, each covered party is separate, and there is substantiallyno risk; any claim is picked up by the instruments purchased to providethe coverage (or the mechanisms, such as short sales, that areemployed).

At step 206, the payment is collected from the covered party. Collectionof the payment preferably is entered into system 10 and noted in a filestored in mass storage device 24. In exchange for the payment, at step207 the provider confers on the covered party the right to sell therequired number of shares at a claim price which is preferably thestarting price. This right, which can be exercised only if there is aprofessional liability triggering event (e.g., an audit failure) withrespect to one or more clients, can be considered a special, or limitedpurpose, put option as discussed above.

After step 207, the system may proceed to step 209 as discussed below,or may optionally proceed (perhaps at a higher cost to the coveredparty) to step 208, where the claim price (i.e., the price at which thelimited purpose put option may be exercised in the event of a claim) isadjusted periodically (e.g., monthly or quarterly) during the coverageperiod. If there is such an adjustment, the provider will have toupgrade the short sale previously made as well as the call option (orother transactions used). The costs of such upgrade would be charged tothe covered party. The covered party might be willing to incur suchcharges because if the stock price increases in the normal course duringthe coverage period, that would increase the baseline from which aclient's stock price could fall, and therefore provide more coverage inthe event a claim is necessary.

If the option to adjust the coverage at step 208 is not selected, orafter the adjustment in step 208 is made, the system proceeds to step209 where it awaits submission of a claim. Although not shown, if thereis no claim during the coverage period, the provider delivers thesecurities to complete the short sale. If the value of the variousstocks in the portfolio has risen, the provider takes advantage of thecall option (paid for by the covered party, so that the provider atworst breaks even) to avoid losing money, while if the values havefallen, the provider may actually make a profit by purchasing the sharesat the lower market price and delivering them at the starting price.

If there is a claim at step 209, then the system proceeds to step 210 todetermine the current (post-event) price of the affected securities.This information preferably is available to system 10 overcommunications lines 34 from an online service. The fall in price,multiplied by the number of shares in the hands of the general public(the management stockholders ordinarily would not have a claim), is themaximum exposure of the covered party in a claim for professionalmalpractice.

Once the exposure has been determined, the system proceeds to test 211to determine whether or not there are enough shares of the affectedclient in the coverage portfolio to cover the exposure. If so, thesystem proceeds to step 212, where the covered party's right to sell theaffected shares at their starting price or other claim price (oroptional adjusted starting or claim price (step 208)) is honored. Theparty will presumably by the shares at their new diminished post-eventprice. This trading in a client's shares, especially after aprofessional liability triggering event, may result in ethical or otherlegal problems, and for this reason, as discussed above, the coveredparty may be the professional's insurer rather than the professional.

If at test 211 it is determined that the affected shares alone will notcover the exposure (because, e.g., the covered party bought enough unitsto cover a 50% decrease, but the decrease was greater), then the systemproceeds to test 213 to determine if other, unaffected companies havedecreased in value in the course of normal market fluctuations. If not,the system returns to step 212 and the covered party must be satisfiedwith the partial coverage that was purchased.

However, if at test 213 it is determined that other companies havedecreased in value, then the system proceeds to step 214, where thenumber of shares in other clients needed to cover the exposure isdetermined (recognizing that even the maximum available number of sharesstill may not cover all the exposure). The system then proceeds to step215 where the covered party's right to sell shares in both the affectedclient, and any unaffected clients that have declined in value, ishonored.

From either step 212 or step 215, the system proceeds to step 216, wherethe coverage provider exercises the right to deliver the shares,acquired from the covered party at the starting price or other claimprice, at the starting price or other agreed delivery price. Theprovider thus breaks even on these shares, or makes a small profit orloss if the there is a differential between the claim price and thedelivery price (where either or both are not equal to the startingprice). The system ends the method after step 216.

FIGS. 3 and 4 show one preferred embodiment of a method 300 according toinvention by which the system 10 of the invention may carry out step 202of FIG. 2 to determine the minimum variance portfolio. The system beginsat step 301 by constructing a variance-covariance matrix of the publiclytraded clients with respect to which coverage is to be provided. Thematrix is an n-by-n matrix of coefficients a_(ij) (i=1. . . n, j=1. . .n) representing the relationship of the price of the ith securityrelative that of the jth security, as explained above. Thesecoefficients are determined by market relationships which may beavailable to system 10 from an online service via communications line34, or from a mass storage device 24, such as a CD-ROM that is updatedperiodically.

After the matrix has been constructed, the system moves on to step 302,where it determines the triggering event index (which in the case of anaccounting firm is the audit failure index) for each pair ofcoefficients a_(ij) /a_(ji). The purpose and meaning of the auditfailure index, and the preferred method of determining the index, aredescribed above. At step 303, each coefficient is preferably multipliedby its respective audit failure index, although some other method oftaking the index into account (such as dividing instead of multiplying)could be used. The audit failure index preferably is the same for a_(ij)as it is for a_(ji).

Next, at step 304, the market value index for each pair of coefficientsa_(ij) /a_(ji) is determined. Again, the significance of the marketvalue index is discussed above, and the preferred method of determiningit is described below in connection with FIG. 5. In this case, thepreferred market value indices for a_(ij) and a_(ji) are different(except, of course, where i=j). At step 305, each coefficient ispreferably multiplied by its respective market value index, althoughsome other method of taking the index into account (such as dividinginstead of multiplying) could be used.

After completion of step 305, an adjusted variance-covariance matrix inaccordance with this invention has been constructed. At step 306, theadjusted matrix is optimized to find the minimum variance portfolio.Optimization techniques for that purpose are well known as describedabove. However, it should be pointed out that almost any optimizationinvolves finding a maximum or minimum, and thus most optimizationtechniques involve, at bottom, some form of differentiation. However,various more sophisticated techniques have been developed to perform therequired optimizations. For example, as described above, a Lagrangemultiplier may be used. And in any computer implemented system, even forperforming a Lagrange multiplier, the ultimate technique used isprobably a numerical technique. Method 300 ends after step 306.

FIG. 4 shows a preferred method 400 for performing market value indexdetermining step 304 (FIG. 3). At step 401, the market values of sharesin the ith and jth companies (or other securities of those companies)are determined from their current market prices and number of shares (orother securities) outstanding and not held by management. The rapidlychanging market price data are most preferably derived from one of themany available online sources via communications line 34 and modem 32.The data on who holds the shares is most preferably derived from massstorage 24 and is updated periodically, although such data may also beavailable online.

At step 402, the system preferably computes the average (i.e., thearithmetic mean) of the market values of the ith and jth companies, bysumming the two market values and dividing by two.

At step 403, the system preferably computes the respective market valueindices for the ijth and jith terms by dividing the ith and jth marketvalues, respectively, by the average market value computed in step 402.Because the average market value must by definition be between the ithand jth market values, it is clear that for whichever of the ith and jthcompanies has the ijth or jith value, the respective ijth or jith marketvalue index will be greater than 1.0 and the other market value indexwill be less than 1.0.

Process 400 ends after step 403. It will be apparent that other measuresof the market value index can be used.

In FIG. 5, which shows a second preferred embodiment of apparatusaccording to the invention, hardware combination 500 replaces CPU 20 formany of the functions performed by process 300. Although a CPU of somekind will still be used for many of the bookkeeping operations of thesystem (billing, collection, etc.), in the embodiment of FIG. 6 many ofthe functions are carried out by special purpose hardware. Although someor all of the dedicated hardware modules could be implemented assingle-program general purpose microprocessors, they may also beimplemented as hard-wired logic (such as appropriately hard-wired gatearrays). As still another alternative, this hardware combination 500could be implemented by a programmable logic device ("PLD"), such as theFLEX 8000™ PLD manufactured by Altera Corporation, of San Jose, Calif.,coupled to an erasable programmable read-only memory ("EPROM"). Oneadvantage to using a PLD-based hardware system would be the ability todynamically reconfigure the hardware components.

Apparatus 500 is built around a communications bus 550 similar to bus 50of FIG. 1. Although not shown in FIG. 5, a CPU similar to CPU 20 mayalso be included in apparatus 500, connected to bus 550. System 500 alsoincludes input/output devices 501 similar to those in system 10,including one or more mass storage devices 24, one or more CRTs 26, oneor more keyboards 28, one or modems 32, and one or more printers 42.

Bookkeeping subsystem 502, whose functions could also be performed by aCPU (not shown) as discussed above, preferably includes anaccounting/arithmetic unit 503 for keeping track of the accounts of thevarious covered parties, a collection system 504 for billing coveredparties and keeping track of their payments, and claim reporting system505 and claim evaluation unit 506 for processing claims by coveredparties. Although each module of subsystem 502 is preferably connecteddirectly to bus 550, the modules 503-506 preferably are alsointerconnected by local bus 507.

Correlation logic 508 is provided to carry out process 300 for derivingthe minimum variance portfolio, and includes correlation evaluator 509for deriving the individual coefficients of the variance-covariancematrix, correlation multiplier/divider unit 510 for determining andapplying the audit failure index and the market value index, andoptimization unit 511 for deriving the minimum variance portfolio fromthe adjusted variance-covariance matrix, all preferably interconnectedby local bus 512 in addition to being connected to bus 550. To theextent necessary, units 509 and 510 use input/output devices 501 via bus550 to obtain the data needed for determining the adjustedvariance-covariance matrix. Unit 511 performs the optimization describedabove, using a differentiation circuit as is well known, or using othermathematical techniques, such as described above, preferably implementedin hardware.

A first trading system 513 secures for the coverage provider the rightsnecessary to deliver the minimum variance portfolio at the requiredfuture date. System 513 includes the logic and communications ability(in conjunction with modems 32 available through bus 550) necessary toexecute the trades needed to secure those rights. Preferably, system 513includes selling unit 514 for making the short sales described above,and buying unit 515 for buying the call option described to shieldagainst unexpected increases in market value, interconnected by localbus 516.

A second trading system 517 creates the rights to be conferred on thecovered party to sell in the future, at the starting price, shares inthe client companies. The necessary data is transferred to subsystem502, as well as to printer 42 for creation of a coverage document, viabus 550.

It will be understood, as set forth above, that although the preferredembodiments of the invention have been described in connection withshares of stock in the client companies, other securities could also beused to carry out the present invention.

Thus it is seen that a system and method are provided that, in the caseof professionals having large numbers of publicly traded corporateclients, are able to use the relative probabilities of different ones ofthose clients suffering a professional liability triggering event andthe likely relative impact of such an event on different clients, toprovide professional liability coverage at either lower cost to theprofessional or higher profits to the provider. One skilled in the artwill appreciate that the present invention can be practiced by otherthan the described embodiments, which are presented for purposes ofillustration and not of limitation, and the present invention is limitedonly by the claims which follow.

What is claimed is:
 1. Apparatus for providing professional liabilitycoverage to a professional, during a coverage period having a startingdate and an ending date, said professional having clients including asubstantial number of publicly traded corporations each having arespective securities price at a respective starting price on saidstarting date, and with respect to whom a professional liabilitytriggering event could cause a decline in said respective securitiesprice, said apparatus comprising:correlation logic for determining arespective number of positions in securities of each of said publiclytraded corporations needed to provide said professional liabilitycoverage, based on market correlation between prices of securities ofsaid publicly traded corporations, and on at least one of (a)probability that a professional liability triggering event will occurrelative to any one or more of said publicly traded corporations, and(b) likely effect of said professional liability triggering event onsaid price of securities of said one or more publicly tradedcorporations; a first trading system for securing at a respective cost aright to deliver at a respective delivery price, at any time at least aslate as said ending date, said respective number of positions insecurities of each of said publicly traded corporations; an arithmeticunit for determining from said respective costs a payment to be chargedto said professional in exchange for said coverage; a second tradingsystem for conferring, in exchange for said payment, a right to sell, ata respective claim price, at any time during said coverage period, up tosaid respective number of positions in securities of any one of saidpublicly traded corporations when there is a professional liabilitytriggering event with respect to any of said publicly tradedcorporations; and a printer for generating a coverage document settingforth said payment and evidencing said right to sell.
 2. The apparatusof claim 1 wherein said delivery price is based on said starting price.3. The apparatus of claim 2 wherein said delivery price is said startingprice.
 4. The apparatus of claim 1 wherein said claim price is based onsaid starting price.
 5. The apparatus of claim 4 wherein said claimprice is said starting price.
 6. The apparatus of claim 4 wherein saidclaim price is said starting price on said starting date and is adjustedperiodically during said coverage period based on market fluctuations ofsaid securities price.
 7. The apparatus of claim 1 wherein said firsttrading system comprises a first trading unit for establishing, on saidstarting date, for later delivery at said delivery price, saidrespective number of positions in securities of each said publiclytraded corporations.
 8. The apparatus of claim 7 wherein said firsttrading unit comprises:a selling unit for selling, on said startingdate, for later delivery at said delivery price, said respective numberof positions in securities of each of said publicly traded corporations;and a buying unit for buying on said starting date, at a respectivecost, a respective option to buy said respective number of positions insecurities of each of said publicly traded corporations at saidrespective buying price at any time during said coverage period.
 9. Theapparatus of claim 8 wherein said buying price is based on said startingprice.
 10. The apparatus of claim 9 wherein said buying price is saidstarting price.
 11. The apparatus of claim 1 wherein said correlationlogic comprises:a correlation evaluator for evaluating, for each one ofsaid publicly traded corporations, a respective one of said marketcorrelations between price of securities of said one of said publiclytraded corporations and price of securities of each respective other oneof said publicly traded corporations; a correlation multiplier unit foradjusting each of said respective correlations by a factor representingrelative probabilities that professional liability triggering eventswill occur relative to correlated ones of said publicly tradedcorporations, and by a factor representing likely relative severity ofeffects of said professional liability triggering events on said pricesof securities of correlated ones of said publicly traded corporations;and an optimization unit for deriving from said adjusted correlations aminimum variance portfolio of positions in securities of said publiclytraded corporations.
 12. The apparatus of claim 11 wherein saidoptimization unit comprises a differentiation unit.
 13. The apparatus ofclaim 1 further comprising:a collection system for collecting saidpayment; a claim reporting system for monitoring for occurrence of aprofessional liability triggering event with respect to saidprofessional and a respective one of said publicly traded corporations;and a claim evaluation unit for, on occurrence of a professionalliability triggering event with respect to said professional: evaluatingeffect of said professional liability triggering event on price ofsecurities of said respective one of said publicly traded corporationsand deriving an exposure therefrom based on a post-event price of saidsecurities, honoring said conferred right to sell, at least up to saidexposure, thereby acquiring positions in securities of at least said oneof said publicly traded corporations at said post-event price, andexercising said right to deliver said positions in securities of atleast said one of said publicly traded corporations at said deliveryprice.
 14. Apparatus for providing professional liability coverage to aplurality of professionals, each professional being covered during arespective coverage period having a starting date and an ending date,each professional having clients including a substantial number ofpublicly traded corporations each having a respective securities priceat a respective starting price on said starting date, and with respectto whom a professional liability triggering event could cause a declinein said respective securities price, said apparatuscomprising:correlation logic for determining, for each saidprofessional, a respective number of positions in securities of each ofsaid publicly traded corporations needed to provide said professionalliability coverage, based on market correlation between prices ofsecurities of said publicly traded corporations, and on at least one of(a) probability that a professional liability triggering event willoccur relative to any one or more of said publicly traded corporations,and (b) likely effect of said professional liability triggering event onsaid price of securities of said one or more publicly tradedcorporations; a first trading system for securing, as to each saidprofessional, at a respective cost, the right to deliver at a respectivedelivery price, at any time at least as late as said ending date, saidrespective number of positions in securities of each of said publiclytraded corporations; an arithmetic unit for determining from saidrespective costs, for each said professional, a payment to be charged inexchange for said coverage; a second trading system for conferring, asto each said professional, in exchange for said payment, a right tosell, at a respective claim price, at any time during said coverageperiod, up to said respective number of positions in securities of anyone of said publicly traded corporations when there is a professionalliability triggering event with respect to any of said publicly tradedcorporations; and a printer for generating a coverage document for eachsaid professional, setting forth said payment and evidencing said rightto sell.
 15. The apparatus of claim 14 further comprising:an accountingunit for establishing an account for each of said professionals; acollection system for collecting said payment and crediting a respectiveone of said accounts; a claim reporting system for monitoring foroccurrence of a professional liability triggering event with respect toany of said professionals and a respective one of said publicly tradedcorporations; and a claim evaluation system for, on occurrence of aprofessional liability triggering event with respect to any one of saidprofessionals: evaluating effect of said professional liabilitytriggering event on price of securities of said respective one of saidpublicly traded corporations and deriving an exposure therefrom based ona post-event price of said securities, honoring said conferred right tosell, at least up to said exposure, thereby acquiring positions insecurities of at least said one of said publicly traded corporations atsaid post-event price, and exercising said right to deliver saidpositions in securities of at least said one of said publicly tradedcorporations at said delivery price.
 16. The apparatus of claim 14wherein said delivery price is based on said starting price.
 17. Theapparatus of claim 16 wherein said delivery price is said startingprice.
 18. The apparatus of claim 14 wherein said claim price is basedon said starting price.
 19. The apparatus of claim 18 wherein said claimprice is said starting price.
 20. The apparatus of claim 18 wherein saidclaim price is said starting price on said starting date and is adjustedperiodically during said coverage period based on market fluctuations ofsaid securities price.
 21. The apparatus of claim 14 wherein said firsttrading system comprises a first trading unit for establishing, on saidstarting date, for later delivery at said delivery price, saidrespective number of positions in securities of each said publiclytraded corporations.
 22. The apparatus of claim 21 wherein said firsttrading unit comprises:a selling unit for selling, on said startingdate, for later delivery at said delivery price, said respective numberof positions in securities of each of said publicly traded corporations;and a buying unit for buying on said starting date, at a respectivecost, a respective option to buy said respective number of positions insecurities of each of said publicly traded corporations at saidrespective buying price at any time during said coverage period.
 23. Theapparatus of claim 22 wherein said buying price is based on saidstarting price.
 24. The apparatus of claim 23 wherein said buying priceis said starting price.
 25. The apparatus of claim 14 wherein saidcorrelation logic comprises:a correlation evaluator for evaluating, foreach one of said publicly traded corporations, a respective one of saidmarket correlations between price of securities of said one of saidpublicly traded corporations and price of securities of each respectiveother one of said publicly traded corporations; a correlation multiplierunit for adjusting each of said respective correlations by a factorrepresenting relative probabilities that professional liabilitytriggering events will occur relative to correlated ones of saidpublicly traded corporations, and by a factor representing likelyrelative severity of effects of said professional liability triggeringevents on said prices of securities of correlated ones of said publiclytraded corporations; and an optimization unit for deriving from saidadjusted correlations a minimum variance portfolio of positions insecurities of said publicly traded corporations.
 26. The apparatus ofclaim 25 wherein said optimization unit comprises a differentiationunit.
 27. Apparatus for financing professional liability insurance for aplurality of professionals, each professional being covered by aninsurer during a respective coverage period having a starting date andan ending date, each professional having clients including a substantialnumber of publicly traded corporations each having a respectivesecurities price at a respective starting price on said starting date,and with respect to whom a professional liability triggering event couldcause a decline in said respective securities price, said apparatuscomprising:correlation logic for determining, for each saidprofessional, a respective number of positions in securities of each ofsaid publicly traded corporations needed to provide said professionalliability coverage, based on market correlation between prices ofsecurities of said publicly traded corporations, and on at least one of(a) probability that a professional liability triggering event willoccur relative to any one or more of said publicly traded corporations,and (b) likely effect of said professional liability triggering event onsaid price of securities of said one or more publicly tradedcorporations; a first trading system for securing, as to each saidprofessional, at a respective cost the right to deliver at a respectivedelivery price, at any time as least as late as said ending date, saidrespective number of positions in securities of each of said publiclytraded corporations; an arithmetic unit for determining from saidrespective costs, for each said professional, a payment to be charged tosaid insurer in exchange for financing said coverage for saidprofessional; a second trading system for conferring on said insurer,for each said professional, in exchange for said payment, a right tosell, at a respective claim price, at any time during said coverageperiod, up to said respective number of positions in securities of anyone of said publicly traded corporations when there is a professionalliability triggering event with respect to said professional and arespective one of said publicly traded corporations; and a printer forgenerating, for delivery to said insurer, a coverage document as to eachsaid professional, setting forth said payment and evidencing said rightto sell.
 28. The apparatus of claim 27 further comprising:an accountingsystem for establishing an account for each insurer; a collection systemfor collecting said payment from each insurer as to a respective one ofsaid professionals and crediting said respective account; a claimreporting system for monitoring for occurrence of a professionalliability triggering event with respect to any of said professionals anda respective one of said publicly traded corporations; and a claimevaluation system for, on occurrence of a professional liabilitytriggering event with respect to any one of said professionals and arespective one of said publicly traded corporations: evaluating effectof said professional liability triggering event on price of securitiesof said respective one of said publicly traded corporations and derivingan exposure therefrom based on a post-event price of said securities,honoring said right conferred on said one of said insurers at least upto said exposure, thereby acquiring from said one of said insurerspositions in securities of at least said one of said publicly tradedcorporations at said post-event price, and exercising said right todeliver said positions in securities of at least said one of saidpublicly traded corporations at said delivery price.
 29. The apparatusof claim 27 wherein said delivery price is based on said starting price.30. The apparatus of claim 29 wherein said delivery price is saidstarting price.
 31. The apparatus of claim 27 wherein said claim priceis based on said starting price.
 32. The apparatus of claim 31 whereinsaid claim price is said starting price.
 33. The apparatus of claim 31wherein said claim price is said starting price on said starting dateand is adjusted periodically during said coverage period based on marketfluctuations of said securities price.
 34. The apparatus of claim 27wherein said first trading system comprises a first trading unit forestablishing, on said starting date, for later delivery at said deliveryprice, said respective number of positions in securities of each saidpublicly traded corporations.
 35. The apparatus of claim 34 wherein saidfirst trading unit comprises:a selling unit for selling, on saidstarting date, for later delivery at said delivery price, saidrespective number of positions in securities of each of said publiclytraded corporations; and a buying unit for buying on said starting date,at a respective cost, a respective option to buy said respective numberof positions in securities of each of said publicly traded corporationsat said respective buying price at any time during said coverage period.36. The apparatus of claim 35 wherein said buying price is based on saidstarting price.
 37. The apparatus of claim 36 wherein said buying priceis said starting price.
 38. The apparatus of claim 27 wherein saidcorrelation logic comprises:a correlation evaluator for evaluating, foreach one of said publicly traded corporations, a respective one of saidmarket correlations between price of securities of said one of saidpublicly traded corporations and price of securities of each respectiveother one of said publicly traded corporations; a correlation multiplierunit for adjusting each of said respective correlations by a factorrepresenting probabilities that professional liability triggering eventswill occur relative to correlated ones of said publicly tradedcorporations, and by a factor representing likely effects of saidprofessional liability triggering events on said prices of securities ofcorrelated ones of said publicly traded corporations; and anoptimization unit for deriving from said adjusted correlations a minimumvariance portfolio of positions in securities of said publicly tradedcorporations.
 39. The apparatus of claim 38 wherein said optimizationunit comprises a differentiation unit.
 40. Apparatus for providingprofessional liability coverage to a professional, during a coverageperiod having a starting date and an ending date, said professionalhaving clients including a substantial number of publicly tradedcorporations each having a respective securities price at a respectivestarting price on said starting date, and with respect to whom aprofessional liability triggering event could cause a decline in saidrespective securities price, said apparatus comprising:means fordetermining a respective number of positions in securities of each ofsaid publicly traded corporations needed to provide said professionalliability coverage, based on market correlation between prices ofsecurities of said publicly traded corporations, and on at least one of(a) probability that a professional liability triggering event willoccur relative to any one or more of said publicly traded corporations,and (b) likely effect of said professional liability triggering event onsaid price of securities of said one or more publicly tradedcorporations; means for securing at a respective cost a right to deliverat a respective delivery price, at any time at least as late as saidending date, said respective number of positions in securities of eachof said publicly traded corporations; means for determining from saidrespective costs a payment to be charged to said professional inexchange for said coverage; means for conferring, in exchange for saidpayment, a right to sell, at a respective claim price, at any timeduring said coverage period, up to said respective number of positionsin securities of any one of said publicly traded corporations when thereis a professional liability triggering event with respect to any of saidpublicly traded corporations; and a printer for generating a coveragedocument setting forth said payment and evidencing said right to sell.41. The apparatus of claim 40 wherein said delivery price is based onsaid starting price.
 42. The apparatus of claim 41 wherein said deliveryprice is said starting price.
 43. The apparatus of claim 40 wherein saidclaim price is based on said starting price.
 44. The apparatus of claim43 wherein said claim price is said starting price.
 45. The apparatus ofclaim 43 wherein said claim price is said starting price on saidstarting date and is adjusted periodically during said coverage periodbased on market fluctuations of said securities price.
 46. The apparatusof claim 40 wherein said means for securing the right to deliver saidrespective number of securities comprises means for establishing, onsaid starting date, for later delivery at said delivery price, saidrespective number of positions in securities of each of said publiclytraded corporations.
 47. The apparatus of claim 46 wherein said meansfor establishing positions comprises:means for selling, on said startingdate, for later delivery at said delivery price, said respective numberof positions in securities of each of said publicly traded corporations;and means for buying on said starting date, at a respective cost, arespective option to buy said respective number of positions insecurities of each of said publicly traded corporations at a respectivebuying price at any time during said coverage period.
 48. The apparatusof claim 47 wherein said buying price is based on said starting price.49. The apparatus of claim 48 wherein said buying price is said startingprice.
 50. The apparatus of claim 40 wherein said means for determiningsaid respective number of positions in securities of each of saidpublicly traded corporations needed to provide said professionalliability coverage comprises:means for evaluating, for each one of saidpublicly traded corporations, a respective one of said marketcorrelations between price of securities of said one of said publiclytraded corporations and price of securities of each respective other oneof said publicly traded corporations; means for adjusting each of saidrespective correlations by a factor representing relative probabilitiesthat professional liability triggering events will occur relative tocorrelated ones of said publicly traded corporations, and by a factorrepresenting likely relative severity of effects of said professionalliability triggering events on said prices of securities of correlatedones of said publicly traded corporations; and means for deriving fromsaid adjusted correlations a minimum variance portfolio of positions insecurities of said publicly traded corporations.
 51. The apparatus ofclaim 40 further comprising:means for collecting said payment; means formonitoring for occurrence of a professional liability triggering eventwith respect to said professional and a respective one of said publiclytraded corporations; and means for, on occurrence of a professionalliability triggering event with respect to said professional: evaluatingeffect of said professional liability triggering event on securities ofsaid respective one of said publicly traded corporations and deriving anexposure therefrom based on a post-event price of said securities,honoring said conferred right to sell, at least up to said exposure,thereby acquiring securities of at least said one of said publiclytraded corporations at said post-event price, and exercising said rightto deliver said positions in securities of at least said one of saidpublicly traded corporations at said delivery price.
 52. Apparatus forproviding professional liability coverage to a plurality ofprofessionals, each professional being covered during a respectivecoverage period having a starting date and an ending date, eachprofessional having clients including a substantial number of publiclytraded corporations each having a respective securities price at arespective starting price on said starting date, and with respect towhom a professional liability triggering event could cause a decline insaid respective securities price, said apparatus comprising:means fordetermining, for each said professional, a respective number ofpositions in securities of each of said publicly traded corporationsneeded to provide said professional liability coverage, based on marketcorrelation between prices of securities of said publicly tradedcorporations, and on at least one of (a) probability that a professionalliability triggering event will occur relative to any one or more ofsaid publicly traded corporations, and (b) likely effect of saidprofessional liability triggering event on said price of securities ofsaid one or more publicly traded corporations; means for securing, as toeach said professional, at a respective cost, the right to deliver at arespective delivery price, at any time at least as late as said endingdate, said respective number of positions in securities of each of saidpublicly traded corporations; means for determining from said respectivecosts, for each said professional, a payment to be charged in exchangefor said coverage; means for conferring, as to each said professional,in exchange for said payment, a right to sell, at a respective claimprice, at any time during said coverage period, up to said respectivenumber of positions in securities of any one of said publicly tradedcorporations when there is a professional liability triggering eventwith respect to any of said publicly traded corporations; and a printerfor generating a coverage document for each said professional, settingforth said payment and evidencing said right to sell.
 53. The apparatusof claim 52 further comprising:means for establishing an account foreach of said professionals; means for collecting said payment andcrediting a respective one of said accounts; means for monitoring foroccurrence of a professional liability triggering event with respect toany of said professionals and a respective one of said publicly tradedcorporations; and means for, on occurrence of a professional liabilitytriggering event with respect to any one of said professionals:evaluating effect of said professional liability triggering event onprice of securities of said respective one of said publicly tradedcorporations and deriving an exposure therefrom based on a post-eventprice of said securities, honoring said conferred right to sell, atleast up to said exposure, thereby acquiring positions in securities ofat least said one of said publicly traded corporations at saidpost-event price, and exercising said right to deliver said positions insecurities of at least said one of said publicly traded corporations atsaid delivery price.
 54. The apparatus of claim 52 wherein said deliveryprice is based on said starting price.
 55. The apparatus of claim 54wherein said delivery price is said starting price.
 56. The apparatus ofclaim 52 wherein said claim price is based on said starting price. 57.The apparatus of claim 56 wherein said claim price is said startingprice.
 58. The apparatus of claim 56 wherein said claim price is saidstarting price on said starting date and is adjusted periodically duringsaid coverage period based on market fluctuations of said securitiesprice.
 59. The apparatus of claim 52 wherein said means for securing theright to deliver said respective number of securities comprises meansfor establishing, on said starting date, for later delivery at saiddelivery price, said respective number of positions in securities ofeach of said publicly traded corporations.
 60. The apparatus of claim 59wherein said means for establishing positions comprises:means forselling, on said starting date, for later delivery at said deliveryprice, said respective number of positions in securities of each of saidpublicly traded corporations; and means for buying on said startingdate, at a respective cost, a respective option to buy said respectivenumber of positions in securities of each of said publicly tradedcorporations at a respective buying price at any time during saidcoverage period.
 61. The apparatus of claim 60 wherein said buying priceis based on said starting price.
 62. The apparatus of claim 61 whereinsaid buying price is said starting price.
 63. The apparatus of claim 52wherein said means for determining said respective number of positionsin securities of each of said publicly traded corporations needed toprovide said professional liability coverage comprises:means forevaluating, for each one of said publicly traded corporations, arespective one of said market correlations between price of securitiesof said one of said publicly traded corporations and price of securitiesof each respective other one of said publicly traded corporations; meansfor adjusting each of said respective correlations by a factorrepresenting relative probabilities that professional liabilitytriggering events will occur relative to correlated ones of saidpublicly traded corporations, and by a factor representing likelyrelative severity of effects of said professional liability triggeringevents on said prices of securities of correlated ones of said publiclytraded corporations; and means for deriving from said adjustedcorrelations a minimum variance portfolio of positions in securities ofsaid publicly traded corporations.
 64. Apparatus for financingprofessional liability insurance for a plurality of professionals, eachprofessional being covered by an insurer during a respective coverageperiod having a starting date and an ending date, each professionalhaving clients including a substantial number of publicly tradedcorporations each having a respective securities price at a respectivestarting price on said starting date, and with respect to whom aprofessional liability triggering event could cause a decline in saidrespective securities price, said apparatus comprising:means fordetermining, for each said professional, a respective number ofpositions in securities of each of said publicly traded corporationsneeded to provide said professional liability coverage, based on marketcorrelation between prices of securities of said publicly tradedcorporations, and on at least one of (a) probability that a professionalliability triggering event will occur relative to any one or more ofsaid publicly traded corporations, and (b) likely effect of saidprofessional liability triggering event on said price of securities ofsaid one or more publicly traded corporations; means for securing, as toeach said professional, at a respective cost the right to deliver at arespective delivery price, at any time at least as late as said endingdate, said respective number of positions in securities of each of saidpublicly traded corporations; means for determining from said respectivecosts, for each said professional, a payment to be charged to saidinsurer in exchange for financing said coverage for said professional;means for conferring on said insurer, for each said professional, inexchange for said payment, a right to sell, at a respective claim price,at any time during said coverage period, up to said respective number ofpositions in securities of any one of said publicly traded corporationswhen there is a professional liability triggering event with respect tosaid professional and a respective one of said publicly tradedcorporations; and a printer for generating, for delivery to saidinsurer, a coverage document as to each said professional, setting forthsaid payment and evidencing said right to sell.
 65. The apparatus ofclaim 64 further comprising:means for establishing an account for eachinsurer; means for collecting said payment from each insurer as to arespective one of said professionals and crediting said respectiveaccount; means for monitoring for occurrence of a professional liabilitytriggering event with respect to any of said professionals and arespective one of said publicly traded corporations; and means for, onoccurrence of a professional liability triggering event with respect toany one of said professionals and a respective one of said publiclytraded corporations:evaluating effect of said professional liabilitytriggering event on price of securities of said respective one of saidpublicly traded corporations and deriving an exposure therefrom based ona post-event price of said securities, honoring said right conferred onsaid one of said insurers at least up to said exposure, therebyacquiring from said one of said insurers positions in securities of atleast said one of said publicly traded corporations at said post-eventprice, and exercising said right to deliver said positions in securitiesof at least said one of said publicly traded corporations at saiddelivery price.
 66. The apparatus of claim 64 wherein said deliveryprice is based on said starting price.
 67. The apparatus of claim 66wherein said delivery price is said starting price.
 68. The apparatus ofclaim 64 wherein said claim price is based on said starting price. 69.The apparatus of claim 68 wherein said claim price is said startingprice.
 70. The apparatus of claim 68 wherein said claim price is saidstarting price on said starting date and is adjusted periodically duringsaid coverage period based on market fluctuations of said securitiesprice.
 71. The apparatus of claim 64 wherein said means for securing theright to deliver said respective number of positions in securitiescomprises means for establishing, on said starting date, for laterdelivery at said delivery price, said respective number of positions insecurities of each of said publicly traded corporations.
 72. Theapparatus of claim 71 wherein said means for establishing positionscomprises:means for selling, on said starting date, for later deliveryat said delivery price, said respective number of positions insecurities of each of said publicly traded corporations; and means forbuying on said starting date, at a respective cost, a respective optionto buy said respective number of positions in securities of each of saidpublicly traded corporations at a respective buying price at any timeduring said coverage period.
 73. The apparatus of claim 72 wherein saidbuying price is based on said starting price.
 74. The apparatus of claim73 wherein said buying price is said starting price.
 75. The apparatusof claim 64 wherein said means for determining said respective number ofpositions in securities of each of said publicly traded corporationsneeded to provide said professional liability coverage comprises:meansfor evaluating, for each one of said publicly traded corporations, arespective one of said market correlations between price of securitiesof said one of said publicly traded corporations and price of securitiesof each respective other one of said publicly traded corporations; meansfor adjusting each of said respective correlations by a factorrepresenting probabilities that professional liability triggering eventswill occur relative to correlated ones of said publicly tradedcorporations, and by a factor representing likely effects of saidprofessional liability triggering events on said prices of securities ofcorrelated ones of said publicly traded corporations; and means forderiving from said adjusted correlations a minimum variance portfolio ofpositions in securities of said publicly traded corporations.
 76. Amethod of using a data processing system including a printer to provideprofessional liability coverage to a professional, during a coverageperiod having a starting date and an ending date, said professionalhaving clients including a substantial number of publicly tradedcorporations each having a respective securities price at a respectivestarting price on said starting date, and with respect to whom aprofessional liability triggering event could cause a decline in saidrespective securities price, said method comprising the steps of:usingsaid data processing system, determining a respective number ofpositions in securities of each of said publicly traded corporationsneeded to provide said professional liability coverage, based on marketcorrelation between prices of securities of said publicly tradedcorporations, and on at least one of (a) probability that a professionalliability triggering event will occur relative to any one or more ofsaid publicly traded corporations, and (b) likely effect of saidprofessional liability triggering event on said price of securities ofsaid one or more publicly traded corporations; using said dataprocessing system to buy and/or sell financial instruments for securingat a respective cost a right to deliver at a respective delivery price,at any time at least as late as said ending date, said respective numberof positions in securities of each of said publicly traded corporations;using said data processing system, determining from said respectivecosts a payment to be charged to said professional in exchange for saidcoverage; and using said printer of said data processing system,generating a coverage document conferring, in exchange for said payment,a right to sell, at a respective claim price, at any time during saidcoverage period, up to said respective number of positions in securitiesof any one of said publicly traded corporations when there is aprofessional liability triggering event with respect to any of saidpublicly traded corporations, said coverage document setting forth saidpayment and evidencing said right to sell.
 77. The method of claim 76wherein said delivery price is based on said starting price.
 78. Themethod of claim 77 wherein said delivery price is said starting price.79. The method of claim 76 wherein said claim price is based on saidstarting price.
 80. The method of claim 79 wherein said claim price issaid starting price.
 81. The method of claim 79 wherein said claim priceis said starting price on said starting date and is adjustedperiodically during said coverage period, using said data processingsystem, based on market fluctuations of said securities price.
 82. Themethod of claim 76 wherein said step of securing the right to deliversaid respective number of positions in securities comprises using saiddata processing system to establish, on said starting date, for laterdelivery at said delivery price, said respective number of positions insecurities of each of said publicly traded corporations.
 83. The methodof claim 82 wherein said step of establishing positions comprises:usingsaid data processing system, selling, on said starting date, for laterdelivery at said delivery price, said respective number of positions insecurities of each of said publicly traded corporations; and using aiddata processing system, buying on said starting date, at a respectivecost, a respective option to buy said respective number of positions insecurities of each of said publicly traded corporations at a respectivebuying price at any time during said coverage period.
 84. The method ofclaim 83 wherein said buying price is based on said starting price. 85.The method of claim 84 wherein said buying price is said starting price.86. The method of claim 76 wherein said step of determining saidrespective number of positions in securities of each of said publiclytraded corporations needed to provide said professional liabilitycoverage comprises:using said data processing system, evaluating, foreach one of said publicly traded corporations, a respective one of saidmarket correlations between price of securities of said one of saidpublicly traded corporations and price of securities of each respectiveother one of said publicly traded corporations; using said dataprocessing system, adjusting each of said respective correlations by afactor representing relative probabilities that professional liabilitytriggering events will occur relative to correlated ones of saidpublicly traded corporations, and by a factor representing likelyrelative severity of effects of said professional liability triggeringevents on said prices of securities of correlated ones of said publiclytraded corporations; and using said data processing system deriving fromsaid adjusted correlations a minimum variance portfolio of positions insecurities of said publicly traded corporations.
 87. The method of claim76 further comprising the steps of:using said data processing system toprocess collection of said payment; using said data processing system,monitoring for occurrence of a professional liability triggering eventwith respect to said professional and a respective one of said publiclytraded corporations; and on occurrence of a professional liabilitytriggering event with respect to said professional; using said dataprocessing system, evaluating effect of said professional liabilitytriggering event on price of securities of said respective one of saidpublicly traded corporations and deriving an exposure therefrom based ona post-event price of said securities, honoring said conferred right tosell, at least up to said exposure, using said data processing system toacquire securities of at least said one of said publicly tradedcorporations at said post-event price, and using said data processingsystem, exercising said right to deliver said securities of at leastsaid one of said publicly traded corporations at said delivery price.88. A method for using a data processing system to provide professionalliability coverage to a plurality of professionals, each professionalbeing covered during a respective coverage period having a starting dateand an ending date, each professional having clients including asubstantial number of publicly traded corporations each having arespective securities price at a respective starting price on saidstarting date, and with respect to whom a professional liabilitytriggering event could cause a decline in said respective securitiesprice, said process comprising the steps of:for each saidprofessional:using said data processing system, determining a respectivenumber of positions in securities of each of said publicly tradedcorporations needed to provide said professional liability coverage,based on market correlation between prices of securities of saidpublicly traded corporations, and on at least one of (a) probabilitythat a professional liability triggering event will occur relative toany one or more of said publicly traded corporations, and (b) likelyeffect of said professional liability triggering event on said price ofsecurities of said one or more publicly traded corporations, using saiddata processing system to buy and/or sell financial instruments forsecuring at a respective cost a right to deliver at said respectivestarting price, at any time at least as late as said ending date, saidrespective number of positions in securities of each of said publiclytraded corporations, using said data processing system, determining fromsaid respective costs a payment to be charged in exchange for saidcoverage, and using said printer of said data processing system,generating a coverage document conferring, in exchange for said payment,a right to sell, at a respective claim price, at any time during saidcoverage period, up to said respective number of positions in securitiesof any one of said publicly traded corporations when there is aprofessional liability triggering event with respect to any of saidpublicly traded corporations, said coverage document setting forth saidpayment and evidencing said right to sell; using said data processingsystem, establishing an account for each of said professionals; usingsaid data processing system to process collection of said payment and tocredit a respective one of said accounts; using said data processingsystem, monitoring for occurrence of a professional liability triggeringevent with respect to any of said professionals and a respective one ofsaid publicly traded corporations; and on occurrence of a professionalliability triggering event with respect to any one of saidprofessionals:using said data processing system, evaluating effect ofsaid professional liability triggering event on price of securities ofsaid respective one of said publicly traded corporations and deriving anexposure therefrom based on a post-event price of said securities,honoring said conferred right to sell, as to said one of saidprofessionals, at least up to said exposure, using said data processingsystem to acquire securities of at least said one of said publiclytraded corporations at said post-event price, and using said dataprocessing system, exercising said right to deliver said securities ofat least said one of said publicly traded corporations at said deliveryprice.
 89. The method of claim 88 wherein said delivery price is basedon said starting price.
 90. The method of claim 89 wherein said deliveryprice is said starting price.
 91. The method of claim 88 wherein saidclaim price is based on said starting price.
 92. The method of claim 91wherein said claim price is said starting price.
 93. The method of claim91 wherein said claim price is said starting price on said starting dateand is adjusted periodically during said coverage period, using saiddata processing system, based on market fluctuations of said securitiesprice.
 94. The method of claim 88 wherein said step of securing theright to deliver said respective number of securities comprises usingsaid data processing system to establish, on said starting date, forlater delivery at said delivery price, said respective number ofpositions in securities of each of said publicly traded corporations.95. The method of claim 94 wherein said step of establishing positionscomprises:using said data processing system, selling, on said startingdate, for later delivery at said starting price, said respective numberof positions in securities in each of said publicly traded corporations;and using said data processing system, buying on said starting date, ata respective cost, a respective option to buy said respective number ofpositions in securities of each of said publicly traded corporations ata respective buying price at any time during said coverage period. 96.The method of claim 95 wherein said buying price is based on saidstarting price.
 97. The method of claim 96 wherein said buying price issaid starting price.
 98. The method of claim 88 wherein said step ofdetermining said respective number of positions in securities of each ofsaid publicly traded corporations needed to provide said professionalliability coverage comprises:using said data processing system,evaluating, for each one of said publicly traded corporations, arespective one of said market correlations between price of securitiesof said one of said publicly traded corporations and price of securitiesof each respective other one of said publicly traded corporations; usingsaid data processing system, adjusting each of said respectivecorrelations by a factor representing relative probabilities thatprofessional liability triggering events will occur relative tocorrelated ones of said publicly traded corporations, and by a factorrepresenting likely relative severity of effects of said professionalliability triggering events on said prices of securities of correlatedones of said publicly traded corporations; and using said dataprocessing system, deriving from said adjusted correlations a minimumvariance portfolio of positions in securities of said publicly tradedcorporations.
 99. A method for using a data processing system to financeprofessional liability insurance for a plurality of professionals, eachprofessional being covered by an insurer during a respective coverageperiod having a starting date and an ending date, each professionalhaving clients including a substantial number of publicly tradedcorporations each having a respective securities price at a respectivestarting price on said starting date, and with respect to whom aprofessional liability triggering event could cause a decline in saidrespective securities price, said process comprising the steps of:foreach said professional:using said data processing system, determining arespective number of positions in securities of each of said publiclytraded corporations needed to provide said professional liabilitycoverage, based on market correlation between prices of securities ofsaid publicly traded corporations, and on at least one of (a)probability that a professional liability triggering event will occurrelative to any one or more of said publicly traded corporations, and(b) likely effect of said professional liability triggering event onsaid price of securities of said one or more publicly tradedcorporations, using said data processing system to buy and/or sellfinancial instruments for securing at a respective cost a right todeliver at a respective delivery price, at any time at least as late assaid ending date, said respective number of positions in securities ofeach of said publicly traded corporations, using data processing system,determining from said respective costs a payment to be charged to saidinsurer in exchange for financing said coverage for said professional,and using said printer of said data processing system, generating acoverage document for delivery to said insurer conferring on saidinsurer, in exchange for said payment, a right to sell, at a respectiveclaim price, at any time during said coverage period, up to saidrespective number of positions in securities of any one of said publiclytraded corporations where there is a professional liability triggeringevent with respect to said professional and a respective one of saidpublicly traded corporations, said coverage document setting forth saidpayment and evidencing said right to sell.
 100. The method of claim 99further comprising the steps of:using said data processing system,establishing an account for each insurer; using said data processingsystem to process collection of said payment from each insurer as to arespective one of said professionals and to credit said respectiveaccount; using said data processing system, monitoring for occurrence ofa professional liability triggering event with respect to any of saidprofessionals and a respective one of said publicly traded corporations;and on occurrence of a professional liability triggering event withrespect to any one of said professionals and a respective one of saidpublicly traded corporations:using said data processing system,evaluating effect of said professional liability triggering event onprice of securities of said respective one of said publicly tradedcorporations and deriving an exposure therefrom based on a post-eventprice of said securities, honoring said right conferred on said one ofsaid insurers, at least up to said exposure, using said data processingsystem to acquire from said one of said insurers positions in securitiesof at least said one of said publicly traded corporations at saidpost-event price, and using said data processing system exercising saidright to deliver said positions in securities of at least said one ofsaid publicly traded corporations at said delivery price.
 101. Themethod of claim 99 wherein said delivery price is based on said startingprice.
 102. The method of claim 101 wherein said delivery price is saidstarting price.
 103. The method of claim 99 wherein said claim price isbased on said starting price.
 104. The method of claim 103 wherein saidclaim price is said starting price.
 105. The method of claim 103 whereinsaid claim price is said starting price on said starting date and isadjusted periodically during said coverage period, using said dataprocessing system, based on market fluctuations of said securitiesprice.
 106. The method of claim 99 wherein said step of securing theright to deliver said respective number of securities comprises usingpaid data processing system to establish, on said starting date, forlater delivery at said delivery price, said respective number ofpositions in securities of each of said publicly traded corporations.107. The method of claim 106 wherein said step of establishing positionscomprises:using said data processing system, selling, on said startingdate, for later delivery at said delivery price, said respective numberof positions in securities of each of said publicly traded corporations;and using said data processing system, buying on said starting date, ata respective cost, a respective option to buy said respective number ofpositions in securities of each of said publicly traded corporations ata respective buying price at any time during said coverage period. 108.The method of claim 107 wherein said buying price is based on saidstarting price.
 109. The method of claim 108 wherein said buying priceis said starting price.
 110. The method of claim 99 wherein said step ofdetermining said respective number of positions in securities of each ofsaid publicly traded corporations needed to provide said professionalliability coverage comprises:using said data processing systemevaluating, for each one of said publicly traded corporations, arespective one of said market correlations between price of securitiesin said one of said publicly traded corporations and price of securitiesin each respective other one of said publicly traded corporations; usingsaid data processing system, adjusting each of said respectivecorrelations by a factor representing relative probabilities thatprofessional liability triggering events will occur relative tocorrelated ones of said publicly traded corporations, and by a factorrepresenting likely relative severity of effects of said professionalliability triggering events on said prices of securities of correlatedones of said publicly traded corporations; and using said dataprocessing system, deriving from said adjusted correlations a minimumvariance portfolio of positions in securities of said publicly tradedcorporations.